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This article is cited in 4 scientific papers (total in 4 papers)
Mathematics
Weakly ill-posed problems of integral geometry witch perturbation on polygonal lines
A. H. Begmatov, A. O. Pirimbetov, A. K. Seidullaev Novosibirsk State Technical University, 20, Prospekt K. Marksa, 630073, Novosibirsk, Russia
Abstract:
We study a problem of reconstruction of a function in a strip from their given integrals with known weight function along polygonal lines. We obtained two simply inversion formulas for the solution to the problem. Using these representations we prove uniqueness and existence theorems for solutions and obtain stability estimates of a solution to the problem in Sobolev's spaces and thus show their weak ill-posedness. Then we consider integral geometry problems with perturbation. The uniqueness theorems are proved and stability estimates of solutions in Sobolev spaces are obtained.
Key words:
ill-posed problems, integral geometry problems, integral transforms, inversion formula, uniqueness, existence theorem, weak instability, perturbation.
Citation:
A. H. Begmatov, A. O. Pirimbetov, A. K. Seidullaev, “Weakly ill-posed problems of integral geometry witch perturbation on polygonal lines”, Izv. Saratov Univ. Math. Mech. Inform., 15:1 (2015), 5–12
Linking options:
https://www.mathnet.ru/eng/isu557 https://www.mathnet.ru/eng/isu/v15/i1/p5
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